Pair formation

• Akin E, Losert V (1983) Dynamics of games and genes: discrete versus continuous time. J Math Biol 17: 241–251

  Article  MathSciNet  MATH  Google Scholar 

• Blythe S, Castillo-Chavez C, Palmer JS, Cheng M (1991) Towards a unified theory of mixing and pair formation. Math Biosci 107: 379–405

  Article  MATH  Google Scholar 

• Blythe S, Busenberg S, Castillo-Chavez C (1995) Affinity in paired event probability. Math Biosci 128: 265–284

  Article  MathSciNet  MATH  Google Scholar 

• Busenberg S, Castillo-Chavez C (1991) A general solution of the problem of mixing of subpopulations and its application to risk-and age structured epidemic models for the spread of AIDS. IMA J Math Appl Med Biol 8: 1–20

  Article  MathSciNet  MATH  Google Scholar 

• Castillo-Chavez C, Busenberg S, Gerow K (1991) Pair formation in structured popualtions. In: Goldstein JA et al (eds) Differential equations with applications in biology, physics, and engineering. Lecture Notes in Pure and Applied Mathematics, vol 133, pp 47–65

• Castillo-Chavez C, Huang W (1995) The logistic equation revisited: the two-sex case. Math Biosci 128: 299–316

  Article  MATH  Google Scholar 

• Castillo-Chavez C, Huang W, Li J (1996) On the existence of stable pairing distributions. J Math Biol 34: 413–441

  Article  MathSciNet  MATH  Google Scholar 

• Dietz K, Hadeler KP (1988) Epidemiological models for sexually transmitted diseases. J Math Biol 26: 1–25

  Article  MathSciNet  MATH  Google Scholar 

• Hadeler KP, Waldstätter R, Wörz-Busekros A (1988) Models for pair formation in bisexual populations. J Math Biol 26: 635–649

  Article  MathSciNet  MATH  Google Scholar 

• Hirsch MW, Smith H (2005) Monotone dynamical systems. In: Handbook of differential equations: ordinary differential equations, vol II. Elsevier B.V, Amsterdam, pp 239–357

• Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge University Press, Cambridge

  MATH  Google Scholar 

• Hoppensteadt F (1975) Mathematical theories of populations: demographics, genetics and epidemics. In: Regional Conference Series in Applied Mathematics, vol 20. SIAM, Philadelphia

• Iannelli M, Milner FA, Martcheva M (2005) Gender-structured population modeling: mathematical methods, numerics, and simulations. In: Frontiers in Applied Mathematics, vol 31. SIAM, Philadelphia

• Jacquez JA, Simon CP, Koopman J (1989) Structured mixing: heterogeneous mixing by the definition of activity groups. In: Mathematical and statistical approaches to AIDS epidemiology. Lecture Notes in Biomathematics, vol 83. Springer, Berlin, pp 301–315

• Kendall DG (1949) Stochastic processes and population growth. Roy Statist Soc Ser B 2: 230–264

  MathSciNet  Google Scholar 

• Keyfitz N (1972) The mathematics of sex and marriage. In: Proceedings of the Sixth Berkeley Symposium on Mathematics Statistics and Probability, vol IV. Biology and health, pp 89–108

• Kingman JFC (1961) On an inequality in partial averages. Q J Math Oxford Ser 12(2): 7880

  Google Scholar 

• Morin BR, Castillo-Chavez C, Hsu Schmitz S-F, Mubayi A, Wang X (2010) Notes from the heterogeneous: a few observations on the implications and necessity of affinity. J Biol Dyn 4: 456–477

  Article  MathSciNet  Google Scholar 

• Parlett B (1972) Can there be a marriage function? In: Greville TNT (ed) Population dynamics. Academic Press, New York, pp 89–106

• Prüss J, Schappacher W (1994) Persistent age-distributions for pair formation models. J Math Biol 33: 17–33

  Article  MathSciNet  MATH  Google Scholar 

• Staroverov OV (1977) Reproduction of the structure of population and marriages. Economia i Mat Metody 13: 72–82 (in Russian)

  MathSciNet  Google Scholar 

• Waldstätter R (1990) Models for pair formation with applications to demography and epidemiology. Ph.D. Thesis, University of Tübingen

• Yellin J, Samuelson PA (1974) A dynamical model for human population. Proc Natl Acad Sci USA 71(7): 2813–2817

  Article  MATH  Google Scholar 

• Zacher R (2001) Persistent solutions for age-dependent pair-formation models. J Math Biol 42: 507–531

  Article  MathSciNet  MATH  Google Scholar 

Download references